Upload
dinhkien
View
234
Download
0
Embed Size (px)
Citation preview
15.401
15.401 Finance Theory15.401 Finance TheoryMIT Sloan MBA Program
Andrew W. LoAndrew W. LoHarris & Harris Group Professor, MIT Sloan SchoolHarris & Harris Group Professor, MIT Sloan School
Lectures 8Lectures 8––99: Forward and Futures Contracts: Forward and Futures Contracts
© 2007–2008 by Andrew W. Lo
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 2
Critical ConceptsCritical ConceptsMotivationForward ContractsFutures ContractValuation of Forwards and FuturesApplicationsExtensions and Qualifications
Readings:Brealey, Myers, and Allen Chapters 27
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 3
MotivationMotivationYour company, based in the U.S., supplies machine tools to customers in Germany and Brazil. Prices are quoted in each country’s currency, so fluctuations in the € / $ and R / $ exchange rates have a big impact on the firm’s revenues. How can the firm reduce (or ‘hedge’) these risks?
Your firm is thinking about issuing 10-year convertible bonds. In the past, the firm has issued straight debt with a yield-to-maturity of 8.2%. If the new bonds are convertible into 20 shares of stocks, per $1,000 face value, what interest rate will the firm have to pay on the bonds?
You have the opportunity to buy a mine with 1 million kgs of copper for $400,000. Copper has a price of $2.2 / kg, mining costs are $2 / kg, and you can delay extraction one year. How valuable is the option to delay? Is the mine a good deal?
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 4
MotivationMotivation
Exchange Rates, 1995 – 2003
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
Jan-95 Jan-96 Jan-97 Jan-98 Jan-99 Jan-00 Jan-01 Jan-02 Jan-030.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
Euro / $ (left scale)Real / $ (right scale)
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 5
MotivationMotivation
Caterpillar, 1980 – 1989
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
12.0
1980 1981 1982 1983 1984 1985 1986 1987 1988 198940
50
60
70
80
90
100
110
120
130
140Sales US $
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 6
MotivationMotivationHedging or Speculation?
Alternative Tools?Futures, forwards, options, and swapsInsuranceDiversificationMatch duration of assets and liabilitiesMatch sales and expenses across countries (currency risk)
Should Firms Hedge With Financial Derivatives?“Derivatives are extremely efficient tools for risk management”“Derivatives are financial weapons of mass destruction”
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 7
MotivationMotivationView 1: Hedging is irrelevant (M&M)
Financial transaction, zero NPVDiversified shareholders don’t care about firm-specific risks
View 2: Hedging creates valueEnsures cash is available for positive NPV investmentsReduces need for external financeReduces chance of financial distressImproves performance evaluation and compensation
Examples:Homestake MiningDoes not hedge because “shareholders will achieve maximum benefit from such a policy.”American BarrickHedges aggressively to provide “extraordinary financial stability… offering investors a predictable, rising earnings profile in the future.”Battle Mountain GoldHedges up to 25% because “a recent study indicates that there may be a premium for hedging.”
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 8
MotivationMotivationEvidence*
Random sample of 413 large firmsAverage cashflow from operations = $735 millionAverage PP&E = $454 millionAverage net income = $318 million
57% of Firms Use Derivatives In 1997Small derivative programsEven with a big move (3σ event), the derivative portfolio pays only
$15 million and its value goes up by $31 million
* Guay and Kothari, Journal of Financial Economics, 2003
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 9
MotivationMotivationBasic Types of Derivatives
Forwards and FuturesA contract to exchange an asset in the future at a specified price and time.Options (Lecture 10)Gives the holder the right to buy (call option) or sell (put option) an asset at a specified price.SwapsAn agreement to exchange a series of cashflows at specified prices and times.
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 10
Forward ContractsForward ContractsDefinition: A forward contract is a commitment to purchase at a future
date a given amount of a commodity or an asset at a price agreed on today.
The price fixed now for future exchange is the forward priceThe buyer of the underlying is said to be “long” the forward
Features of Forward ContractsCustomizedNon-standard and traded over the counter (not on exchanges)No money changes hands until maturityNon-trivial counterparty risk
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 11
Forward ContractsForward ContractsExample:
Current price of soybeans is $160/tonTofu manufacturer needs 1,000 tons in 3 monthsWants to make sure that 1,000 tons will be available3-month forward contract for 1,000 tons of soybeans at $165/tonLong side will buy 1,000 tons from short side at $165/ton in 3 months
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 12
Futures ContractsFutures ContractsForward Contracts Have Two Limitations:
IlliquidityCounterparty risk
Definition: A futures contract is an exchange-traded, standardized, forward-like contract that is marked to market daily. This contract can be used to establish a long (or short) position in the underlying asset.
Features of Futures ContractsStandardized contracts:– Underlying commodity or asset– Quantity– Maturity
Exchange tradedGuaranteed by the clearing house—no counter-party riskGains/losses settled daily (marked to market)Margin required as collateral to cover losses
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 13
Futures ContractFutures ContractssExample:NYMEX crude oil (light) futures with delivery in Dec. 2007 at a price of
$75.06 / bbl. on July 27, 2007 with 51,475 contracts tradedEach contract is for 1,000 barrelsTick size: $0.01 per barrel, $10 per contractInitial margin: $4,050Maintenance margin: $3,000No cash changes hands today (contract price is $0) Buyer has a “long” position (wins if prices go up)Seller has a “short” position (wins if prices go down)
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 14
Futures ContractsFutures Contracts
Payoff Diagram$
-6
-4
-2
0
2
4
6
$70 $71 $72 $73 $74 $75 $76 $77 $78 $79 $80
Oil price, Dec07
Long position (buy) Short position (sell)
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 15
Futures ContractsFutures ContractsExample. Yesterday, you bought 10 December live-cattle contracts on the
CME, at a price of $0.7455/lbContract size 40,000 lbAgreed to buy 40,000 pounds of live cattle in DecemberValue of position yesterday:
(0.7455)(10)(40,000) = $298,200No money changed handsInitial margin required (5%−20% of contract value)
Today, the futures price closes at $0.7435/lb, 0.20 cents lower. The value of your position is
(0.7435)(10)(40,000) = $297,400which yields a loss of $800.
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 16
Futures ContractsFutures ContractsWhy Is This Contract Superior to a Forward Contract?
Standardization makes futures liquidMargin and marking to market reduce default riskClearing-house guarantee reduces counter-party risk
HedgersFutures Clearing
CorpSpeculators
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 17
Valuation of Forwards and FuturesValuation of Forwards and Futures
What Determines Forward and Futures Prices?Forward/futures prices ultimately linked to future spot pricesNotation:
Ignore differences between forward and futures price for now
Two ways to buy the underlying asset for date-T delivery1. Buy a forward or futures contract with maturity date T2. Buy the underlying asset and store it until T
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 18
Valuation of Forwards and FuturesValuation of Forwards and Futures
Date Forward Contract Outright Asset Purchase
0
T
Total Cost at T
Pay $0 for contract with forward price $F0,T
Borrow $S0
Pay $S0 for AssetPay $F0,T
Own assetPay back $S0(1+r)T
Pay cumulative storage costs (if any)Deduce cumulative “convenience yield” (if any)Own asset
$F0,T $S0(1+r)T + net storage costs
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 19
Valuation of Forwards and FuturesValuation of Forwards and Futures
Date Forward Contract Outright Asset Purchase
t
T
Total Cost at T
Pay $0 for contract with forward price $Ft,T
Borrow $St
Pay $St for AssetPay $Ft,T
Own assetPay back $St(1+r)T-t
Pay cumulative storage costs (if any)Deduce cumulative “convenience yield” (if any)Own asset
$Ft,T $S0(1+r)T-t + net storage costs
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 20
Valuation of Forwards and FuturesValuation of Forwards and FuturesWhat Determines Forward/Futures Prices?
Difference between the two methods:– Costs (storage for commodities, not financials)– Benefits (convenience for commodities, dividends for financials)
By no arbitrage (Principal P1), these two methods must cost the same
GoldEasy to store (negligible costs of storage)No dividends or benefitsTwo ways to buy gold for T– Buy now for St and hold until T– Buy forward at t, pay Ft,T at T and take delivery at T
No-arbitrage requires that
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 21
Valuation of Forwards and FuturesValuation of Forwards and FuturesGasoline
Costly to store (let c be percentage cost per period)Convenience yield does exist (let y be percentage yield per period)Not for long-term investment (like gold), but for future useTwo ways to buy gasoline for T– Buy now for St and hold until T– Buy forward at t, pay Ft,T at T and take delivery at T
No-arbitrage requires that
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 22
Valuation of Forwards and FuturesValuation of Forwards and FuturesFinancials
Let underlying be a financial asset– No cost to store (the underlying asset)– Dividend or interest on the underlying
Example: Stock index futures– Underlying are bundles of stocks, e.g., S&P, Nikkei, etc.– Futures settled in cash (no delivery)– Let the annualized dividend yield be d; then:
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 23
Valuation of Forwards and FuturesValuation of Forwards and FuturesExample:Gold quotes on 2001.08.02 are
Spot price (London fixing) $267.00/ozOctober futures (CMX) $269.00/ozWhat is the implied interest rate?
F = S0(1 + rf)2/12
rf = (F/S0)6 − 1 = 4.58%
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 24
Valuation of Forwards and FuturesValuation of Forwards and FuturesExample:Gasoline quotes on 2001.08.02:
Spot price is 0.7760Feb 02 futures price is 0.73306-month interest rate is 3.40%What is the annualized net convenience yield (net of storage costs)?
0.7330 = (0.7760)(1+ 0.0340− y)6/12
y = 1.0340 −µ0.7330
0.7760
¶2= 14.18%
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 25
Valuation of Forwards and FuturesValuation of Forwards and FuturesExample:
The S&P 500 closed at 1,220.75 on 2001.08.02The S&P futures maturing in December closed at 1,233.50Suppose the T-bill rate is 3.50%What is the implied annual dividend yield?
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 26
ApplicationsApplicationsIndex Futures Have Many Advantages
Since underlying asset is a portfolio, trading in the futures market is easier than trading in cash marketFutures prices may react quicker to macroeconomic news than the index itselfIndex futures are very useful for:– Hedging market risk in block purchases and underwriting– Creating synthetic index fund– Portfolio insurance
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 27
ApplicationsApplicationsExample:You have $1 million to invest in the stock market and you have decided to
invest in the S&P 500. How should you do this?One way is to buy the S&P 500 in the cash market:– Buy the 500 stocks, weights proportional to their market caps
Another way is to buy S&P futures:– Put the money in your margin account– Assuming the S&P 500 is at 1,000 now, number of contract to buy:
(value of a futures contract is $250 times the S&P 500 index)
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 28
ApplicationsApplicationsExample (cont):
As the S&P index fluctuates, the future value of your portfolio (in $MM) is given by the following table (ignoring interest payments and dividends):
Suppose you a diversified portfolio of large-cap stocks worth $5MM and are now worried about equity markets and would like to reduce your exposure by 25%—how could you use S&P 500 futures to implement this hedge?– (Short)sell 5 S&P 500 futures contracts (why 5?)
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 29
ApplicationsApplicationsExample (cont):
Compare hedged and unhedged portfolio (in $MM):
Fluctuations have been reducedAs if 25% of the portfolio has been shifted to cash
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 30
Extensions and QualificationsExtensions and Qualifications
Interest-rate, bond, and currency futures are extremely popularSingle-stock futures are gaining liquidityVolatility futures recently launched (VIX)
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 31
Key PointsKey Points
Forward and futures contracts are zero-NPV contracts when initiatedAfter initiation, both contracts may have positive/negative NPVFutures contracts are “marked to market” every dayFutures and forwards are extremely liquidHedging and speculating are important applications of futures/forwards
© 2007–2008 by Andrew W. LoLecture 8–9: Forwards and Futures
15.401
Slide 32
Additional ReferencesAdditional ReferencesBrealey, R., Myers, S., and F. Allen, 2006, Principles of Corporate Finance. New York: McGraw-Hill Irwin.
Guay, W. and S. Kothari, 2003, “How Much Do Firms Hedge with Derivatives?,” Journal of Financial Economics 70, 423–461.
Siegel, D. and D. Siegel, 1990, The Futures Market: Arbitrage, Risk Management, and Portfolio Strategies. Hinsdale, IL: Dryden Press.
MIT OpenCourseWarehttp://ocw.mit.edu
15.401 Finance Theory I Fall 2008
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.